Question

question
write the following expression in simplest radical form.
\\(\left(\sqrt3{9r^5}\
ight)\left(\sqrt3{3r^8}\
ight)\\)
answer attempt 1 out of 2

Explanation:

Step1: Multiply the radicands

$$\sqrt[3]{9r^5} \cdot \sqrt[3]{3r^8} = \sqrt[3]{9r^5 \cdot 3r^8}$$

Step2: Simplify the product inside

$$\sqrt[3]{27r^{5+8}} = \sqrt[3]{27r^{13}}$$

Step3: Factor into perfect cubes

$$\sqrt[3]{27 \cdot r^{12} \cdot r} = \sqrt[3]{27} \cdot \sqrt[3]{r^{12}} \cdot \sqrt[3]{r}$$

Step4: Evaluate perfect cube roots

$$3 \cdot r^4 \cdot \sqrt[3]{r}$$

Answer:

$3r^4\sqrt[3]{r}$